A GTX 970 or R9 390 (I'd lean toward the 390/390X for more usable memory) would probably suffice, except for a few newer and/or unoptimized games, like Everybody's Gone to the Rapture or Quantum Break. If you aren't turning down any settings and need 60fps, though, you'd have to get a faster, more expensive card to guarantee that for all or close to all games, even at less than 1080p.
If you have only a handful of games you play, it may be easier to get to the magic 60fps level without spending too much cash... it's just hard to say for sure, especially as the newest games (and upcoming DX12 titles) may or may not give you a perfect, lag-free experience maxed at 1050 on anything less than the 980 Ti or Fury series level.